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2026年北京大学强基计划笔试部分试题解析日拱一卒,争取做完一半先.一共是20道题.其实受制于考试时间,大部分试题难度并不高.复数问题,也给你直接硬算了一下,不过强烈建议在复平面内考虑问题.原点和点(2,2)连线刚好是y=x,这意味着这两个复数的辐角应该关于45度对称,再结合其模长均为3即可顺利求解.对中国剩余定理的直接考察.注意到x-1和x+1的最大公因数是2,于是他们不能同时被3或5整除,这就大大缩减了范围.注意mod2的时候要稍微讨论一下.其实两个部分的讨论可以合并,这里注意到不可能有2个及以上的零,那么不妨设的内容可以进一步写为"x>=0,y>=0,z<=0且至多只能取等一次".这样后续的放缩中的大于号即可取到等.谁能帮我找找原题在哪里(如果没记错的话是AIME考过),但这显然是一个复平面上的问题,麻烦的地方在于注意到(x^2026-1)/(x-1)是可以直接写出来的.也是一个三角函数解三角形的问题,需要先注意到A的值,最后都用C来表示会比较好算.温州还是哪里的模拟考考过的问题.根据对称性可知切线的倾斜角是45度,利用柯西不等式的等号成立条件就可以快速求解了.
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